CN117299530A - A single-machine driven energy-saving horizontal elliptical vibrating screen and its parameter determination method - Google Patents
A single-machine driven energy-saving horizontal elliptical vibrating screen and its parameter determination method Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
- B07B—SEPARATING SOLIDS FROM SOLIDS BY SIEVING, SCREENING, SIFTING OR BY USING GAS CURRENTS; SEPARATING BY OTHER DRY METHODS APPLICABLE TO BULK MATERIAL, e.g. LOOSE ARTICLES FIT TO BE HANDLED LIKE BULK MATERIAL
- B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
- B07B1/28—Moving screens not otherwise provided for, e.g. swinging, reciprocating, rocking, tilting or wobbling screens
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B07—SEPARATING SOLIDS FROM SOLIDS; SORTING
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- B07B1/00—Sieving, screening, sifting, or sorting solid materials using networks, gratings, grids, or the like
- B07B1/46—Constructional details of screens in general; Cleaning or heating of screens
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Abstract
The invention belongs to the technical field of vibration screening devices, and discloses a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof. The single machine driving energy-saving type horizontal elliptical vibrating screen comprises: the vibration exciter, the outer body, the inner body, the shearing rubber spring and the vibration isolation spring; the vibration isolation spring is connected with the foundation and the main body; the vibration exciter is positioned at the mass center of the outer mass body, the vibration exciter consists of an eccentric rotor and an induction motor, and rotates around the center of the rotation axis of the vibration exciter, so that exciting force is generated, the inner mass body generates certain vibration intensity, the motion track of the inner mass body is elliptical motion, the inner mass body with corresponding quantity can be installed according to the use requirement, the productivity is improved, the power consumption is reduced, and the engineering application value of the vibration exciter is realized.
Description
Technical Field
The invention relates to the technical field of vibration screening devices, in particular to a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof.
Background
The technology of the vibrating screen at the present stage gradually tends to be mature, and is widely applied to the sand and aggregate industry, mines, steel mills, foods, chemical industry, petroleum, tunnel engineering and the like, and classification of various materials is realized. Accordingly, there are many kinds of shakers including those that screen in a single frequency drive, those that employ a single body far super resonance technique, and the like, but these shakers suffer from various drawbacks. For example, the working frequency of the single-body vibrating screen in CN102744203a is far beyond the resonance frequency, the required exciting force is large, so that the power consumption is also increased, and when the vibrating screen starts and stops to pass through the resonance region, the equipment can generate large vibration, so that the machine can run unstably and is easy to damage, and the service life of the machine is reduced. Thereby causing the waste of resources and improving the production cost. In addition, the existing material screening mode mostly needs to be screened for multiple times, materials with different granularity can be separately collected, screening efficiency is low, the situation that coarse and fine materials are mixed after screening is still generated, and production requirements cannot be met. Therefore, it is necessary to design a vibrating screen device to improve the screening quality and to allow efficient production.
Disclosure of Invention
The invention aims to solve the technical problem of providing a single-machine-driven energy-saving horizontal elliptical vibrating screen and a parameter determination method thereof, and a double-mass high-frequency vibrating fine screen utilizing a sub-resonance technology is used, so that the screening area of the whole machine can be increased, the energy consumption can be reduced, and the screening efficiency can be improved.
The vibration exciter on the exosome is used as a research object, a dynamic model is firstly established, and a Lagrange equation is applied to calculate a motion differential equation of the system. Because the system is driven by a single machine, the system is stable, and then the natural frequency of the main vibration system is obtained. And solving steady-state responses of the inner and outer plastids in the x and y directions and an elliptic orbit equation of the inner plastid. And finally, the high-order natural frequency and the low-order natural frequency of the system under the action of external excitation are obtained, so that the working range of the machine is determined. And simulating corresponding working parameters and motion tracks through simulation.
The technical scheme of the invention is as follows: a single machine driven energy efficient horizontal elliptical vibrating screen comprising: the vibration exciter 5, the outer body 2, the inner body 3, the shear spring 4 and the vibration isolation spring 1; the vibration isolation springs 1 are symmetrically distributed and connected with the foundation 6 and the outer body 2; the vibration exciter 5 comprises an eccentric rotor and an induction motor, and is positioned at the mass center of the outer body 2; the vibration exciter 5 rotates around the center of the rotation axis of the vibration exciter to generate exciting force, and drives the horizontal elliptical vibrating screen system to generate vibration intensity and the inner body 3 to realize elliptical motion; the inner plastid comprises a plurality of plastids, and each plastid is connected to the inner base of the outer plastid 3 through a plurality of shear springs 4; all shear springs 4 have the same inclination angle; the adjacent plastids are equidistant.
The outer body 2 is a vibrating screen body, and the inner body 3 is a screen; the shear springs 4 are distributed at two ends of the plastid; the material inlet and the material outlet of the vibrating screen body are symmetrically distributed at the origin of the body center of the vibrating screen body.
When the inclination angle of the shear spring 4 is 0-90 degrees, the vibration exciter 5 rotates anticlockwise, the feeding port is positioned at the upper right part of the vibrating screen body, and the discharging port is positioned at the lower left part of the vibrating screen body; when the inclination angle of the shearing spring is 90-180 degrees, the vibration exciter 5 rotates clockwise, the feeding port is positioned at the upper left part of the vibrating screen body, and the discharging port is positioned at the lower right part of the vibrating screen body.
A single machine driving energy-saving type horizontal elliptical vibrating screen parameter determining method comprises the following steps:
step 1, establishing a dynamic model and a system motion differential equation;
setting a fixed coordinate Oxy, the rotation center of the exciter 5 being O, the corresponding phase being expressed asThe whole horizontal elliptic vibrating screen system has three degrees of freedom, which are divided into x-direction vibration, y-direction vibration and swinging psi around the mass center;
the number of x, y, ψ,for generalized coordinates, based on Lagrange's equation, the differential equation of motion of the horizontal elliptical vibrating screen system is derived as follows:
wherein;
M 1 ＝m 1 +m 2 +m 3 +...+m n ，M 2 ＝m 0 +m v ，M＝M 1 +M 2
β＝0°-90°
l x ＝l 1 ·cosβ,l y ＝l 2 ·cosβ
wherein M is the total mass of the horizontal elliptic vibrating screen system; m is m v Is the mass of the exosomes; m is m 0 The mass of the eccentric rotor of the vibration exciter; m is m i I=1, 2,3 … n for the mass of the screen; j is the moment of inertia of the whole horizontal elliptical vibrating screen system; j (J) 0 The moment of inertia of the vibration exciter; j (J) m The rotational inertia of the induction motor is that of an inner body, an outer body and a vibration exciter; l (L) e Equivalent radius of gyration for horizontal elliptic vibrating screen system; r is the eccentricity of the vibration exciter; f (f) 0 Is the shaft damping coefficient of the induction motor; t (T) 0 Electromagnetic output torque of the induction motor; beta is the installation angle of the shear spring; k (k) x ，k ψ Spring rates of the horizontal elliptical vibrating screen system in the x and psi directions, respectively; k, k y Spring rates of the inner mass and the outer mass in the y direction respectively; f (f) x ，f ψ Damping coefficients of the horizontal elliptic vibrating screen system in the x and psi directions are respectively set; f (f) 1y ,f 2y Damping coefficients of the inner mass and the outer mass in the y direction are respectively shown; l (L) 1 The linear distance from the connecting point of the vibration isolation spring 6 and the outer body to the mass center of the vibrating screen; l (L) 2 The horizontal distance from the connecting point of the vibration isolation spring 1 and the outer body to the mass center of the vibrating screen; beta is the inclination angle of the shear spring;is a first order time derivative;Is the second time derivative;
step 2, calculating the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system;
and step 3, calculating the high-order natural frequency and the low-order natural frequency of the horizontal elliptical vibrating screen system.
The natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system are calculated as follows;
in steady state, consider nothing in equation (2)k x And k y All are smaller than k, regardless of the damping constant f of the exosomes 2y ；
In summary, the formulas (1) and (2) are simplified to
In the middle of
M 1 ′＝M 1 ，
Ignoring k y Therefore, it is
M 2 ′＝M 2
Finishing (6) and (7) to obtain:
in the method, in the process of the invention,
y 3 ＝y 1 -y 2
wherein M is 3 Is the induction quality of the horizontal elliptic vibrating screen system, y 3 Is y 1 、y 2 Is a relative displacement of (2);
the natural frequency omega of the horizontal elliptical vibrating screen system is deduced according to (8) n ；
In the method, in the process of the invention,
from the above formula, when ω m0 /ω n When=1, the horizontal elliptical vibrating screen system resonates at this time, at this time y 12 Having a maximum value, i.e. amplitude at this point
The absolute motion response of the horizontal elliptical shaker system in the x, y and ψ directions is derived by transfer function methods as follows:
when epsilon a ε cj +ε b ε d At the time of > 0 "the total number of the cells,
when epsilon a ε cj +ε b ε d When the number of the groups is less than 0,
from the above, the maximum displacement of the endosome in the x-direction isMaximum displacement in the y direction is
The elliptic orbit equation of the endosome is as follows:
in the method, in the process of the invention,
wherein x is 1 ，y 1 ，ψ 1 Absolute motion responses of the endosome in the x, y, ψ directions, respectively.
The calculated high-order natural frequency and low-order natural frequency of the horizontal elliptical vibrating screen system are specifically as follows;
the eigenvalue equation of the horizontal elliptical vibrating screen system obtained by the formulas (1) and (2) and the two corresponding higher-order natural frequencies and the lower-order natural frequencies are respectively expressed as
(k-ω 2 M 1 )(k+k y -ω 2 M 2 )-k 2 The solution of =0 (14),
in the method, in the process of the invention,b＝M 1 (k y +k)+M 2 k，c＝[M 1 (k+k y )] 2 +(M 2 k) 2 +2M 1 M 2 k(k-k y )；
ignoring parameter k 1y After that, omega is obtained 1 ＝ω 0 The method comprises the steps of carrying out a first treatment on the surface of the From the above, two frequencies of the horizontal elliptical vibrating screen system are known, and ω 2 ＜ω 1 ＝ω 0 The method comprises the steps of carrying out a first treatment on the surface of the Adjusting the operating frequency of the motor to be less than the natural frequency omega of the horizontal elliptical vibrating screen system 0 Realizing the sub-sharing of the vibrating screenVibrating.
The invention has the beneficial effects that:
(1) The invention adopts the single-machine driven double-plastid horizontal elliptic vibrating screen, has unique high efficiency and working performance, and compared with the traditional direct driving design, the double-plastid vibrating screen can lead the movement amplitude of the screen to be larger under the same condition, thereby being capable of reducing the power consumption better. Furthermore, the elliptical screening movement has a higher screening efficiency than the horizontal screening movement. In addition, different numbers of screens with different granularities can be arranged according to requirements to realize the simultaneous screening of multiple granularities, and the working efficiency is improved;
(2) The sub-resonance double-mass vibrating screen adopts the sub-resonance technology, the vibration frequency is smaller than the natural frequency of a vibration system, sub-resonance occurs when the equipment works, and compared with the single-mass vibrating screen, the sub-resonance double-mass vibrating screen has the advantages of smaller required exciting force and low power consumption. The starting and stopping processes do not pass through a high-order resonance area, so that the damage to the machine is reduced, and the service life is longer;
(3) Through the vibration exciting shear rubber spring and the vibration isolation spring that set up, can realize driving bigger screen frame with very little exciting force, enlarge working amplitude through the vibration excitation spring system to can not influence the performance of screening performance along with the change of material load, vibration isolation spring not only can support the vibration source box, can reduce the dynamic load who gives foundation or structure frame moreover.
Drawings
FIG. 1 is a diagram of a dynamic model of a horizontal elliptical vibrating screen system.
In the figure: 1. a vibration isolation spring; 2. an exosome; 3. an endoplasm; 4. a shear spring; 5. a vibration exciter; 6. and (3) foundation.
Meaning of each parameter in the figure: o-the center of the entire system;-exciter rotational phase angle; m is m 0 -mass of the exciter; r-eccentricity of the exciter; k (k) x -spring rate in x-direction; k (k) y -y directionUpper spring rate; k-the stiffness of the shear rubber spring; beta is the inclination angle of the shearing rubber spring; n-number of screens.
FIG. 2 (a) is a diagram of motor speed simulation results;
FIG. 2 (b) is a diagram showing the simulation result of the motion trail of the inner and outer plastids;
FIG. 2 (c) is a graph showing the results of the y-direction displacement simulation of the inner and outer masses;
fig. 2 (d) is a graph showing the result of the displacement simulation in the x direction of the liposome.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the vibration exciter 5 is composed of a motor-driven eccentric rotor and is arranged at the mass center of the vibrating screen body; the exciter 5 rotates at a fixed speed when operated. The vibration exciter 5 is connected with the vibrating screen body so as to enable the vibrating screen body to perform circular motion; the inner screen 3 is fixed on the outer box body through a shearing rubber spring 4 inclined at a certain angle, different numbers of screens 3 can be arranged according to different use requirements, and the distances between each screen 3 are equal and symmetrically distributed in the vertical direction so as to keep overall balance. The feed inlet of shale shaker is located the upper right side of outside screen cloth 2, and the discharge gate is located the lower left side of outside screen cloth 2. The vibration isolation springs 1 are 4 in number, are installed at the bottom of the outer box body 2 in the front-back and left-right mode, and are installed on the foundation 6.
The vibration exciter rotates anticlockwise during operation, so that the movement direction of the outer box body is the same as that of the outer box body, the inner screen mesh moves in an elliptical manner due to a certain angle of the shearing rubber spring connecting the screen mesh and the box body, and materials automatically move leftwards in the screening process due to the movement direction, so that the arrangement positions of the material inlet and the material outlet are also determined.
The double-mass body has two natural frequencies, and the working interval of the vibrating screen is arranged between the two natural frequencies, so that the aim of sub-resonance work is fulfilled, the vibration exciter rotates for one circle, the screen mesh completes one screening movement, and the sub-resonance movement of the vibration exciter, namely the sub-resonance movement of the vibrating screen, is realized by changing the parameters of the driving motor.
Because the vibrating screen is a double-mass vibrating screen, two natural frequencies can be generated under the action of external excitation, and in order to realize the sub-resonance, the working range of the vibrating screen is selected between the high-order natural frequency and the low-order natural frequency so as to achieve the purpose of the sub-resonance. In addition, the system itself is stable due to the single drive, so the stability of the system is not considered.
To further analyze the system characteristics, numerical analysis was performed.
The system parameters were set as follows: m is m 1 +m 2 +...+m n ＝350kg，m＝700kg，m 0 ＝20kg，J＝500kg·m 2 ，k x ＝k y ＝550kN/m，k＝11800kN/m，k ψ ＝450kN/rad，f x ＝f y ＝6.27kN·s/m，f ψ =5.20 kn·s/rad, r=0.15 m. According to the above parameters and the parameter determining method, the system natural frequency can be obtained as follows: omega x ＝ω y = 224.89rad/s, motor type three-phase squirrel cage, 50hz,380v,6-pole,0.75kW, rated speed 980r/min.
Claims (7)
1. The energy-saving type elliptical vibrating screen driven by a single machine is characterized in that the energy-saving type elliptical vibrating screen driven by the single machine comprises: the vibration isolator comprises a vibration exciter (5), an outer body (2), an inner body (3), a shear spring (4) and a vibration isolation spring (1); the vibration isolation springs (1) are symmetrically distributed and connected with the foundation (6) and the outer body (2); the vibration exciter (5) comprises an eccentric rotor and an induction motor, and is positioned at the mass center of the outer body (2); the vibration exciter (5) rotates around the center of the rotation axis of the vibration exciter to generate exciting force, the horizontal elliptical vibrating screen system is driven to generate vibration intensity, and the inner body (3) is driven to realize elliptical motion; the inner plastid comprises a plurality of plastids, and each plastid is connected to an inner base of the outer plastid (3) through a plurality of shear springs (4); all shear springs (4) have the same inclination angle; the adjacent plastids are equidistant.
2. The single machine driving energy-saving type horizontal elliptic vibrating screen according to claim 1, wherein the outer body (2) is a vibrating screen body, and the inner body (3) is a screen; the shearing springs (4) are distributed at two ends of the plastid; the material inlet and the material outlet of the vibrating screen body are symmetrically distributed at the origin of the body center of the vibrating screen body.
3. The single machine driving energy-saving type horizontal elliptical vibrating screen according to claim 1 or 2, wherein when the inclination angle of the shear spring (4) is 0-90 degrees, the vibration exciter (5) rotates anticlockwise, the feeding port is positioned at the upper right side of the vibrating screen body, and the discharging port is positioned at the lower left side of the vibrating screen body; when the inclination angle of the shearing spring is 90-180 degrees, the vibration exciter (5) rotates clockwise, the feeding port is positioned at the upper left part of the vibrating screen body, and the discharging port is positioned at the lower right part of the vibrating screen body.
4. A method for determining parameters of a single machine-driven energy-saving type horizontal elliptical vibrating screen as claimed in claim 1 or 2, comprising the steps of:
step 1, establishing a dynamic model and a system motion differential equation;
setting a fixed coordinate Oxy, wherein the rotation center of the vibration exciter (5) is O, and the corresponding phase is expressed asThe whole horizontal elliptic vibrating screen system has three degrees of freedom, which are divided into x-direction vibration, y-direction vibration and swinging psi around the mass center;
the number of x, y, ψ,for generalized coordinates, based on Lagrange's equation, the differential equation of motion of the horizontal elliptical vibrating screen system is derived as follows:
wherein;
M 1 ＝m 1 +m 2 +m 3 +...+m n ，M 2 ＝m 0 +m v ，M＝M 1 +M 2
β＝0°-90°
l x ＝l 1 ·cosβ,l y ＝l 2 ·cosβ
wherein M is the total mass of the horizontal elliptic vibrating screen system; m is m v Is the mass of the exosomes; m is m 0 The mass of the eccentric rotor of the vibration exciter; m is m i I=1, 2,3 … n for the mass of the screen; j is the moment of inertia of the whole horizontal elliptical vibrating screen system; j (J) 0 The moment of inertia of the vibration exciter; j (J) m The rotational inertia of the induction motor is that of an inner body, an outer body and a vibration exciter; l (L) e Equivalent radius of gyration for horizontal elliptic vibrating screen system; r is the eccentricity of the vibration exciter; f (f) 0 Is the shaft damping coefficient of the induction motor; t (T) 0 Electromagnetic output torque of the induction motor; k (k) x ，k ψ Spring rates of the horizontal elliptical vibrating screen system in the x and psi directions, respectively; k, k y Spring rates of the inner mass and the outer mass in the y direction respectively; f (f) x ，f ψ Damping coefficients of the horizontal elliptic vibrating screen system in the x and psi directions are respectively set; f (f) 1y ,f 2y Damping coefficients of the inner mass and the outer mass in the y direction are respectively shown; l (L) 1 The linear distance from the connecting point of the vibration isolation spring (6) and the outer body to the mass center of the vibrating screen; l (L) 2 The horizontal distance from the connecting point of the vibration isolation spring (1) and the outer body to the mass center of the vibrating screen; beta is the inclination angle of the shear spring;is a first order time derivative;Is the second time derivative;
step 2, calculating the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system;
and step 3, calculating the high-order natural frequency and the low-order natural frequency of the horizontal elliptical vibrating screen system.
5. The method for determining parameters of a single machine-driven energy-saving type horizontal elliptical vibrating screen according to claim 4, wherein the natural frequency, steady-state response and trajectory equation of the horizontal elliptical vibrating screen system are calculated as follows;
in steady state, consider nothing in equation (2)k x And k y All are smaller than k, regardless of the damping constant f of the exosomes 2y ；
In summary, the formulas (1) and (2) are simplified to
In the middle of
M 1 ′＝M 1 ，
Ignoring k y Therefore, it is
M 2 ′＝M 2
Finishing (6) and (7) to obtain:
in the method, in the process of the invention,
y 3 ＝y 1 -y 2
wherein M is 3 Is the induction quality of the horizontal elliptic vibrating screen system, y 3 Is y 1 、y 2 Is a relative displacement of (2);
the natural frequency omega of the horizontal elliptical vibrating screen system is deduced according to (8) n ；
In the method, in the process of the invention,
from the above formula, when ω m0 /ω n When=1, the level is at this timeElliptical vibrating screen system resonates, at which time y 12 Having a maximum value, i.e. amplitude at this point
The absolute motion response of the horizontal elliptical shaker system in the x, y and ψ directions is derived by transfer function methods as follows:
when epsilon a ε cj +ε b ε d At the time of > 0 "the total number of the cells,
when epsilon a ε cj +ε b ε d When the number of the groups is less than 0,
from the above, the maximum displacement of the endosome in the x-direction isMaximum displacement in the y direction is
6. The method for determining parameters of a single machine driven energy-saving type horizontal elliptical vibrating screen according to claim 5, wherein an elliptical trajectory equation of the inner body is:
in the method, in the process of the invention,
wherein x is 1 ，y 1 ，ψ 1 Absolute motion responses of the endosome in the x, y, ψ directions, respectively.
7. The method for determining parameters of a single machine driving energy-saving type horizontal elliptical vibrating screen according to claim 5, wherein the calculated high-order natural frequency and low-order natural frequency of the horizontal elliptical vibrating screen system are specifically;
the eigenvalue equation of the horizontal elliptical vibrating screen system and the two corresponding higher-order natural frequencies and the lower-order natural frequencies obtained by the formulas (1) and (2) are respectively expressed as (k-omega) 2 M 1 )(k+k y -ω 2 M 2 )-k 2 ＝0 (14)
Solving to obtain
In the middle of
b＝M 1 (k y +k)+M 2 k，
c＝[M 1 (k+k y )] 2 +(M 2 k) 2 +2M 1 M 2 k(k-k y )
Ignoring parameter k 1y After that, omega is obtained 1 ＝ω 0 The method comprises the steps of carrying out a first treatment on the surface of the From the above, two frequencies of the horizontal elliptical vibrating screen system are known, and ω 2 ＜ω 1 ＝ω 0 The method comprises the steps of carrying out a first treatment on the surface of the Adjusting the operating frequency of the motor to be less than the natural frequency omega of the horizontal elliptical vibrating screen system 0 The sub-resonance work of the vibrating screen is realized.
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| 韩彦龙;贺斌;赵春雨;: "双质体振动筛自同步理论研究", 燕山大学学报, no. 05, 30 September 2017 (2017-09-30) * |
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